The garment industry in Vietnam is one of the country's strongest industries in the world. However, the production process still encounters problems regarding scheduling that does not equate to an optimal process. The paper introduces a production scheduling solution that resolves the potential delays and lateness that hinders the production process using integer programming and order allocation with a make-to-order manufacturing viewpoint. A number of constraints were considered in the model and is applied to a real case study of a factory in order to view how the tardiness and lateness would be affected which resulted in optimizing the scheduling time better. Specifically, the constraints considered were order assignments, production time, and tardiness with an objective function which is to minimize the total cost of delay. The results of the study precisely the overall cost of delay of the orders given to the plant and successfully propose a suitable production schedule that utilizes the most of the plant given. The study has shown promising results that would assist plant and production managers in determining an algorithm that they can apply for their production process.

In according to a report in 2017, Vietnam has about 2,800 clothing enterprises, most of which are located in Ho Chi Minh City and Ha Noi. In the past, around 70% of Vietnam's clothing depended on using imported raw materials such as fabrics and fibers from China due to the Vietnam's regulation about controlling tightly the dyeing segment. In 2001, when the trading relationships between Vietnam and Western countries were established, exporting Vietnamese clothing began to develop. In 2016, according to WTO, it is reported that around $28 billion of clothing were exported, which is the third largest value in global apparel exporter, after China and Bangladesh. The 2017 US Fashion Industry Benchmarking Study indicated that Vietnam is the second apparel sourcing country, after China. In recent years, with the development of technology, the human's standard of living tends to be high considerably, and the needs of clothing is continuously changing. Many enterprises deal with a considerable number of challenges with regard to the change in demands of customers, shorter product life cycle. In addition, customer requirements for specialized and customized production tend to increased. Therefore, to survive in the intensely competitive market place and quickly respond to this changing environment, many firms have begun considering a change in service mode and improving their production scheduling to meet the deadline committed to customers, otherwise the firms can face to a significant loss of goodwill and penalty. It is obvious that more companies tend to offer mass customization service to customers. Unlike in make-to-stock (MTS), in which the finished goods are hold in inventory as a buffer to deal with the variations in customer demand, make-to-order (MTO) operation starts performing an order only after it has been received. The most important aspect in MTO is the effective and efficient utilization of available capacity to meet customer demands. In make-to-order manufacturing, customer satisfaction is always the key to evaluate the success of the performance of production planning and scheduling. In specific, a typical measure of customer satisfaction is the customer service level which is the fraction of customer orders finished on or before their due dates.

In this study, the authors will consider the problem of an apparel company which provide customized products. The main objective of this paper is to minimize the cost of tardy orders by allocating the order to produce for each day. After that, based on the final optimal result, the authors will propose the days needed working overtime. Finally compare the cost of penalty and cost of overtime to choose the better option. From that apparel company can increase its production efficiency, reduce the loss of order, and improve customer's satisfaction.

There have been multiple studies about the application of mathematical programming in the solving optimization problems in manufacturing systems [

The Chen et al. [

The production planning problem was also presented by Sadeghi Naieni Fard et al. [

Ben Hmida et al. [

Shabtay [

Lee [

Lin et al. [

Huang et al. [

Chen et al. [

Sawik [

This research differs from the above-mentioned literature in many aspects. The objective considered is to minimize the cost due to completing the orders after their due date base on the production cost and the sales price on the contract with the customers. Many existing literatures just consider the number of tardy orders or the profit. In addition, there are several papers which study how to control and set the due date for orders. However, this research focusses on the way to allocate the order for production with the constant due dates so that the manager can have an overview about daily utilization and decide the necessary day for overtime to meet the due date commitment.

In this section, the authors built a research process to solve the current problem of factory X mentioned on the problem statement section (

The first step in the process is to identify a problem. Through the observation the operation of factory, the primary problem of factory is responding to the customer's orders is overdue date and pay a constant amount of penalty cost or loss the whole order.

After defining the problem, the most important step is establishing the long-term objective which can be applied to company for more than one year. The objective of the models in this paper applied to solve the problem of company is to assign customer orders to planning periods to minimize the cost of tardy orders. From that, company can offer the overtime day to achieve a high customer satisfaction by meeting customers due dates and get a low penalty.

The model will be built with the constraint depending on the availability and capacity of company and be compatible with the development of the technology. Apparel company currently set the customer service level is the top priority. Therefore, the authors applied a linear integer model with the primary objective of minimizing the total cost of tardiness by allocating all orders (

The model will be built with the constraint depending on the availability and capacity of company and be compatible with the development of the technology. Apparel company currently set the customer service level is the top priority. Therefore, the authors applied a linear integer model with the primary objective of minimizing the total cost of tardiness by allocating all orders (

To ensure the validity of the model, the collection process is needed to plane carefully before such as the number of team member for collection and the high concentration is required during the collection period to make sure the high reliability of data.

Running the model with a small sized problem is to test and fix model, then apply the real data collected to the model for the result.

From the result, the authors can compare the improvement of tardiness after and before using the scheduling model.

After analyzing results, the authors propose some alternatives method can be used and the predict of the application of my model.

There have been many studies applying integer programming for production scheduling problems. In fact, in day today life, many software have been developed to solve the optimization problem like IBM CPLEX Optimizer. Through literature review, there is enough scope for the improvement in the production scheduling environment when the processing time is not constant. This suggests and motivates me to apply integer linear programming and CPLEX optimization which will provide the best quality solutions and reduces the computational burden.

To solve the problem statement of this study, the following basic assumptions are used:

All machines at one workstation are same speed and functionality;

The available day to start each order is known before;

All orders arrive at the beginning of the planning horizon;

The quantity of split order is not less than 30% of the total quantity of order.

The inputs of the model are shown in

Group name | Input data |
---|---|

Order | Quantity |

Inventory | Capacity |

Flow | Number of production line |

The annotations of the model are defined as follows:

The input parameters are denoted as follows:

The decision variable notations are as follows:

The objective is to minimize the total cost of delay value:

Subject to the following constrains:

Constrain

Constraint

Constraint

In this case study, numerical data of apparel company are showed to illustrate possible applications of approach. The authors will consider a set of total 28 customer orders recorded in August 2019 for testing this model (

Order | Quantity | Due date (day) | Available date (day) |
---|---|---|---|

1 | 500 | 25 | 1 |

2 | 1000 | 23 | 10 |

3 | 1000 | 23 | 7 |

4 | 500 | 25 | 9 |

5 | 1000 | 25 | 8 |

6 | 1000 | 23 | 7 |

7 | 500 | 25 | 12 |

8 | 500 | 23 | 7 |

9 | 1500 | 23 | 12 |

10 | 1000 | 25 | 9 |

11 | 1000 | 21 | 12 |

12 | 1500 | 26 | 10 |

13 | 1500 | 21 | 7 |

14 | 1000 | 26 | 7 |

15 | 1000 | 25 | 1 |

16 | 1500 | 23 | 7 |

17 | 1000 | 25 | 7 |

18 | 1000 | 21 | 10 |

19 | 1500 | 21 | 8 |

20 | 1500 | 26 | 7 |

21 | 2000 | 21 | 7 |

22 | 2000 | 23 | 14 |

23 | 1500 | 23 | 8 |

24 | 2000 | 21 | 8 |

25 | 2500 | 25 | 7 |

26 | 1500 | 21 | 14 |

27 | 2000 | 24 | 1 |

28 | 2000 | 23 | 8 |

Moreover, the processing time unit of each product type bases on the characteristics of that products and the number of stages that are required for that process. The authors collected the unit processing time of each stage and the processing time of each unit equals the sum of the processing times of stages required. These collected data had measure unit as second unit. After that, we transfer second unit into day unit base on the working time of labor. The working time is 10 h per day including the lunch time with 1 h. Therefore, the processing time for each product unit is calculated according to the below formula:

The unit processing times in day are shown in

Order | Unit processing time (s) | Unit processing time (day) |
---|---|---|

1 | 65 | 0.00201 |

2 | 70 | 0.00216 |

3 | 77 | 0.00238 |

4 | 85 | 0.00262 |

5 | 75 | 0.00231 |

6 | 80 | 0.00247 |

7 | 90 | 0.00278 |

8 | 78 | 0.00241 |

9 | 79 | 0.00244 |

10 | 74 | 0.00228 |

11 | 72 | 0.00222 |

12 | 61 | 0.00188 |

13 | 82 | 0.00253 |

14 | 72 | 0.00222 |

15 | 83 | 0.00256 |

16 | 80 | 0.00247 |

17 | 90 | 0.00278 |

18 | 80 | 0.00247 |

19 | 85 | 0.00262 |

20 | 84 | 0.00259 |

21 | 68 | 0.00210 |

22 | 75 | 0.00231 |

23 | 87 | 0.00269 |

24 | 82 | 0.00253 |

25 | 77 | 0.00238 |

26 | 88 | 0.00272 |

27 | 67 | 0.00207 |

28 | 72 | 0.00222 |

For each order, the classification about indivisible and divisible orders will be different according to the productivity for each type of product, which is calculated using the following formula:

The order division result is shown in

Order type | Order number |
---|---|

Divisible order | Order 1 to Order 20 |

Indivisible order | Order 21 to Order 28 |

Besides, when there is an order completed after due date, then there are two kinds of paying results. The company will pay penalty cost with a certain penalty rate, or the customer cancel the order, the company thus will bear whole the production cost. The costs of order delay of each order are shown in

Order | Cost name | Value (VND) |
---|---|---|

1 | Cancel order | 100,250,000 |

2 | Paying 11% of whole contract for delaying within 14 days | 42,068,840 |

3 | Paying 11% of whole contract for delaying within 14 days | 41,041,220 |

4 | Paying 11% of whole contract for delaying within 14 days | 22,327,910 |

5 | Paying 11% of whole contract for delaying within 14 days | 33,132,000 |

6 | Cancel order | 150,200,000 |

7 | Paying 11% of whole contract for delaying within 14 days | 18,645,000 |

8 | Paying 11% of whole contract for delaying within 14 days | 22,327,910 |

9 | Paying 11% of whole contract for delaying within 14 days | 65,340,000 |

10 | Cancel order | 215,477,000 |

11 | Paying 11% of whole contract for delaying within 14 days | 38,544,000 |

12 | Paying 11% of whole contract for delaying within 14 days | 66,036,630 |

13 | Paying 11% of whole contract for delaying within 14 days | 66,495,000 |

14 | Paying 11% of whole contract for delaying within 14 days | 42,900,000 |

15 | Paying 11% of whole contract for delaying within 14 days | 42,900,000 |

16 | Paying 11% of whole contract for delaying within 14 days | 71,107,410 |

17 | Cancel order | 213,018,000 |

18 | Paying 11% of whole contract for delaying within 14 days | 44,330,000 |

19 | Paying 11% of whole contract for delaying within 14 days | 61,116,000 |

20 | Paying 11% of whole contract for delaying within 14 days | 66,036,630 |

21 | Paying 11% of whole contract for delaying within 14 days | 82,082,440 |

22 | Cancel order | 350,400,000 |

23 | Paying 11% of whole contract for delaying within 14 days | 55,605,000 |

24 | Paying 11% of whole contract for delaying within 14 days | 79,420,000 |

25 | Paying 11% of whole contract for delaying within 14 days | 117,159,900 |

26 | Paying 11% of whole contract for delaying within 14 days | 55,330,110 |

27 | Paying 11% of whole contract for delaying within 14 days | 81,488,000 |

28 | Cancel order | 391,000,000 |

In addition, it is assumed that the percentage of productivity is 100%, the daily limited capacity of production is calculated as:

The characteristics of integer programming model are summarized in

Variables | Binary | Constraints | Non-zero coefficients | Z_{sum} |
CPU runtime (s) |
---|---|---|---|---|---|

2381 | 671 | 1837 | 6647 | 33,132,000 | 21.84 |

After running the model, the optimal tardy order is 1 order. That is the order 5. From the result of model, company can see the day which high utilization and offer the day that workers need to work overtime so that there is no late order.

Day | Utilization (%) | Day | Utilization (%) |
---|---|---|---|

1 | 0.00 | 16 | 99.38 |

2 | 64.04 | 17 | 100.00 |

3 | 72.38 | 18 | 100.00 |

4 | 0.00 | 19 | 100.00 |

5 | 0.00 | 20 | 91.44 |

6 | 56.10 | 21 | 92.59 |

7 | 92.59 | 22 | 100.00 |

8 | 100.00 | 23 | 100.00 |

9 | 99.69 | 24 | 70.60 |

10 | 98.15 | 25 | 92.09 |

11 | 94.91 | 26 | 97.22 |

12 | 98.38 | 27 | 57.87 |

13 | 100.00 | 28 | 0.00 |

14 | 99.65 | 29 | 0.00 |

15 | 100.00 | 30 | 0.00 |

From the table of the utilization show that the utilization from day 7 to day 26 is quite high. This prove that on this period, most of orders have enough resources to be ready for production before due date. In addition, due to reduce the level of inventory of the finished products, the orders should not be finished too early from the due dates. Therefore, the authors will choose day 21 and day 22 nearly to the end of the total completion time on which workers will work overtime 2 h extra. As a result, the number of tardy orders now equal zero and there is no fining cost happened.

The overtime cost paying for worker is 20,000 VND/hour. The estimated number of workers needed for each production flow is 5 workers so the total number of workers working overtime is about 20 workers. Therefore, the total cost of working overtime (TCO) for two days is 800,000 VND/hour. Since TCD > TCO, the better option should be working overtime.

With the amount of penalty of tardy order from the result of model, input to the extended model to identify the minimum completion time for total 28 orders. The result of the extended model indicates that although the time range the authors consider is 30 days (one month), the total time needed to complete total 26 orders with 1 tardy order and the penalty cost is 33,132,000 VND.

The research is conducted to study how to minimize the cost of delay completion of orders in the ideal condition by building a linear integer program. In this study, the current problems in operation of garment company are analyzed. The main idea focuses on production scheduling problem. A linear integer model for assignment and allocating orders with the aim to minimize the cost of tardy orders is built. With the proposed model, plant and production managers can apply suitably in order to optimize their production process in order to plan ahead should there will be an abundance of customer orders that reaches the plant using contemporary and realistic constraints that can be applied in any circumstances. The model still needs to consider a number of different aspects such as resources utilization or cost of materials when applied in the scheduling process which could be a further study in the future. This model can be applicable from management perspective. The result of extended model can provide for manager the optimal completion time and have the new schedule for the orders next period.

The authors acknowledge and appreciate the support of Van Lang University, Vietnam, National Kaohsiung University of Science and Technology, Taiwan.